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RafaelArutjunjan committed Dec 24, 2021
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6 changes: 3 additions & 3 deletions Project.toml
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name = "DerivableFunctions"
uuid = "b86e32d1-1d4d-4472-88d2-1980e9d19c92"
authors = ["Rafael Arutjunjan"]
version = "0.1.2"
version = "0.1.3"

[deps]
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
Expand All @@ -16,9 +16,9 @@ Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
DataFrames = "1"
FiniteDifferences = "0.11, 0.12"
ForwardDiff = "0.10"
ModelingToolkit = "5, 6, 7"
ModelingToolkit = "5 - 8"
ReverseDiff = "1.8, 1.9"
Symbolics = "2, 3, 4"
Symbolics = "2 - 4"
Zygote = "0.6"
julia = "1"

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4 changes: 2 additions & 2 deletions docs/src/Operators.md
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Clearly, this simplified implementation features some redundant evaluations of the inverse metric and could be made more efficient.
Nevertheless, it nicely illustrates how succinctly complex real-world examples can be formulated.

Given the metric tensor ``g(\\theta, \\phi) = \\mathrm{diag}(1, \\mathrm{sin}(\\theta))`` induced by the canonical embedding of ``S^2`` into ``\\mathbb{R}^3`` with spherical coordinates, it can be shown that the Ricci scalar assumes a constant value of ``R=2`` everywhere on ``S^2``.
Given the metric tensor induced by the canonical embedding of ``S^2`` into ``\\mathbb{R}^3`` with spherical coordinates, it can be shown that the Ricci scalar assumes a constant value of ``R=2`` everywhere on ``S^2``.
```julia
S2metric((θ,ϕ)) = [1.0 0; 0 sin(θ)^2]
2 RicciScalar(S2metric, rand(2); ADmode=Val(:ForwardDiff)) RicciScalar(S2metric, rand(2); ADmode=Val(:ReverseDiff))
```

(In this particular instance, due to a term ``\\mathrm{cos}(\\theta) \\, \\mathrm{sin}(\\theta) / (\\mathrm{sin}(\\theta))^2`` in the `ChristoffelSymbol` where the ``\\mathrm{sin}(\\theta)`` in the numerator does not cancel with the identical term in the denominator, the symbolic computation does not recognize the fact that the final expression can be simplified to yield exactly ``R=2``.)
(In this particular instance, due to a term in the `ChristoffelSymbol` where the `sin` in the numerator does not cancel with the identical term in the denominator, the symbolic computation does not recognize the fact that the final expression can be simplified to yield exactly ``R=2``.)
```julia
using Symbolics; @variables p[1:2]
RicciScalar(S2metric, p)
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@RafaelArutjunjan
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Registration pull request created: JuliaRegistries/General/51191

After the above pull request is merged, it is recommended that a tag is created on this repository for the registered package version.

This will be done automatically if the Julia TagBot GitHub Action is installed, or can be done manually through the github interface, or via:

git tag -a v0.1.3 -m "<description of version>" e7218b16c73acbdc4c57c3ea37d44bd34a7d94ef
git push origin v0.1.3

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